Light follows Geodesics-Spacetime-Big Bang-Time dilation

[chester20080]

I have these questions:
1) Why must light always move along a geodesic line? What is the principle behind that?
2) A second question about spacetime:
We mostly depict or imagine spacetime as a net of flexible fiber that extends everywhere as a plane as we see it.. As we are looking it, what exists above that plane or underneath it? Are there infinite such nets intertwined that take up and make up the whole spacetime? I guess that's only our picture for spacetime..
3) Right after big bang it is believed that inflation occurred with a speed far greater than speed of light. I know that this is said to be allowed by relativity since no information was transmitted with that speed. But everything is information and even the dimension of space and time that took up the "thing" that enclosed big bang can be considered as bits of information so the upper limit for speed should be applied. What is wrong?
4) And finally I want to ask about time dilation. For example the twin paradox. To sum it up, the one travels with great speed in space and after Earth years he comes back young etc.. While his brother is old and everything has changed.
But. We assign his speed with reference to the brother on Earth (reference frame A which we consider still). But also, if we put a reference frame on the space traveler (B , which is moving with regards to A, but is still according to the traveler), he sees the brother on Earth to be moving with the great speed, since speed is relative. But finally the traveler will be young and experienced time dilation and not the brother on earth! What happens?

 

[Grinkle]

1) Why must light always move along a geodesic line? What is the principle behind that?

If one looks at gravity as something that bends geodesics of spacetime away from Euclidean-straight lines, and one accepts that light will move in a straight line, then it makes sense that light will follow the gravity-induced geodesic. Does it not?

 

[chester20080]

If one looks at gravity as something that bends geodesics of spacetime away from Euclidean-straight lines, and one accepts that light will move in a straight line, then it makes sense that light will follow the gravity-induced geodesic. Does it not?

Actually , why a geodesic is the shortest way? If we have a semi folded surface, the shortest way of moving from one point of the surface to another , staying on this surface, is indeed a geodesic. But we could move between these points via the in between space not belonging to the surface. Or via another dimension. Is that wrong theoretically?
And (considering euclidean geometry and no gravity bending ) why should light always move in a straight line and not in any other way?

What about the other three questions?

 

[Ibix]

1. We model light (and indeed, anything not subject to a force) following geodesics because that's an accurate model of what they do. We have no more fundamental reason than that, although quantum gravity may change that when we work it out. We don't model anything leaving spacetime because we never see anything leaving spacetime.

2. We do not picture spacetime like that. We model it as a smooth pseudo-Riemannian manifold. Some popularisations try to draw that as a distorted grid, but that isn't really helpful. There's no evidence of anything outside the spacetime manifold at this time.

3. Not a clue.

4. There are many threads on this - try searching this forum. The short version is that the elapsed time depends on the "length" of the path through spacetime. The two twins follow different paths so have different elapsed times.

 

[Nugatory]

) Right after big bang it is believed that inflation occurred with a speed far greater than speed of light. I know that this is said to be allowed by relativity since no information was transmitted with that speed. But everything is information and even the dimension of space and time that took up the "thing" that enclosed big bang can be considered as bits of information so the upper limit for speed should be applied. What is wrong?

Not only is no information being transmitted at superluminal speeds, nothing is moving at superluminal speeds. You'll find a slightly more prosaic example when you consider that there are galaxies so distant that there recession velocity due to the expansion of the universe is greater than ##c##. You will find many threads explaining how this works and how it is consistent with special relativity here and in the Cosmology subforum.

 

[Nugatory]

We mostly depict or imagine spacetime as a net of flexible fiber that extends everywhere as a plane as we see it.. As we are looking it, what exists above that plane or underneath it? Are there infinite such nets intertwined that take up and make up the whole spacetime? I guess that's only our picture for spacetime..

Actually , why a geodesic is the shortest way? If we have a semi folded surface, the shortest way of moving from one point of the surface to another, staying on this surface, is indeed a geodesic. But we could move between these points via the in between space not belonging to the surface. Or via another dimension. Is that wrong theoretically?

That's actually the same question twice...
A geodesic on the surface of the Earth is a great circle, and it is the shortest distance between two points if you're constrained to stay on the surface of the earth. You are right that we could find a shorter path by taking advantage of the third dimension - we drill a tunnel in a straight line between the two points through the bulge of the earth, and that would be shorter than the great circle route.

However we can only do that because the the two-dimensional surface of the Earth is a subset of a larger three-dimensional space (literally a subset - every point on the surface of the Earth is also a point in the three-dimensional ball that is the earth, and there are points in that ball that are not part of the surface). However, our four-dimensional spacetime is not embedded in a fifth dimension - the points that make up that spacetime are all the points there are, and there's no fifth dimension to take a shortcut through.

These depictions and imaginations that you're talking about are illustrations and analogies - they're just an aid for visualizing how the geometry of the surface works. It's an unfortunate side-effect that we can't draw such a picture without introducing an extra dimension - but that dimension isn't really there and we can't use it.

 

[chester20080]

About the inflation comment:

Maybe you are referring to the expansion of spacetime itself.
However, anything can be considered as information.
Even that expansion itself.
For instance I can claim that the information that was carried was that space got bigger.
Anything.
Also someone could claim about that, that there was no observation made whatsoever so nothing was violated. On the contrary, I could say that we can't prove that no observation was made or it was indeed made. Perhaps a Boltzmann brain made it,we can't know,everything is purely hypothetical and relies on the anthropic principle.

About the spacetime and geodesics comment:

The fact that we don't have access to a fifth dimension is why. It doesn't mean it isn't there. Maybe we are limited to access it. And since there is a good chance that higher dimensions exist,we could say that our four dimensional perceived universe is a subset to a higher dimensional universe and there the classic geodesic as we now know it , the shortest way would be different , via the in between space as I mentioned.
In these theories about higher dimensions, are there references to the future of geodesics there? What could they be?

About the time dilation question:

Can someone give a link of similar posts or answers?
The path traveled is also considered to be relative, as the traveler can see the brother on Earth to cover a long path as he sees him move.

 

[Nugatory]

About the time dilation question:

Can someone give a link of similar posts or answers?
The path traveled is also considered to be relative, as the traveler can see the brother on Earth to cover a long path as he sees him move.

You will find a pretty decent description in the "spacetime diagram" section of the Twin Paradox FAQ: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

The length of the paths are not relative. Using the coordinates of the stay-at-home twin, the moving twin starts at the point A (x=0,t=0), travels at .5c for one year to reach the point B (x=.5,t=1), and then spends another year moving to point C (x=0, t=2) - all times measured in years and distances in lightyears. The stay-at-home twin's path through spacetime runs directly from point A to point C.

The length of the direct path from point A to point C is two years. The length of the path from A to B is ##\sqrt{3}/2## years, as is the length of the path from B to C... So the traveler has taken the shorter path: A to B plus B to C is ##\sqrt{3}/2+\sqrt{3}/2=\sqrt{3} < 2##. (Google for "spacetime interval" and "timelike" to see how I did that).

Although different frames will assign different coordinate values to those three points, the distances they calculate will always come out the same; this is an example of an "invariant", something that is the same in all reference frames.

Any more discussion of the twin paradox should go in its own thread. But do not write another word about it until you have studied that FAQ in detail and looked at some of the many other threads here.

 

[Nugatory]

However, anything can be considered as information.

Anything can be considered as information, but there's one particular definition of "information" that's used in the statement about information not traveling faster than light... so if you're going to look for whether that principle is being violated you can't use a different and much less precise definition and then claim to have discovered a violation.

Also someone could claim about that, that there was no observation made whatsoever so nothing was violated. On the contrary, I could say that we can't prove that no observation was made or it was indeed made. Perhaps a Boltzmann brain made it,we can't know,everything is purely hypothetical and relies on the anthropic principle.

Aside from some popsci-fueled misunderstandings about quantum mechanics (which wouldn't be applicable to relativity even if they weren't bogus) in physics things are true or not true whether they're observed or not. You are free to argue this proposition, but not here - we're about physics.

About the spacetime and geodesics comment:
The fact that we don't have access to a fifth dimension is why. It doesn't mean it isn't there. Maybe we are limited to access it. And since there is a good chance that higher dimensions exist,we could say that our four dimensional perceived universe is a subset to a higher dimensional universe and there the classic geodesic as we now know it , the shortest way would be different , via the in between space as I mentioned.
In these theories about higher dimensions, are there references to the future of geodesics there? What could they be?

There's not even a ghost of a hint that higher dimensions of the sort that you're thinking about exist (and under the PF rules if you claim otherwise you must provide a link to a serious peer-reviewed paper supporting that claim).

The only theories about higher dimensions that I am aware of are Kaluza-Klein and its variants (google will find some good stuff) and the modern supersymmetry and string theories with their extra degrees of freedom expressed as extra dimensions. They cannot be used in the way that you're thinking about, to shortcut a geodesic path through spacetime. You may have to take my word for this though, as the only even slightly layman-friendly explanation of how these "dimensions" work is in an example in Hartle's GR textbook "Gravity: An Introduction to Einstein's General Relativity", and that's written for last-year undergrads on their way to a PhD program, so maybe not much help in a B-level thread.

 

[Nugatory]

1) Why must light always move along a geodesic line? What is the principle behind that?

As Ibix has already mentioned, it's not just light - everything that's not subject to some external force follows a geodesic line through spacetime. There's no obvious reason why it has to be that way, and it may be that the only answer is that that's how the universe works - it has to work some way, and this just happens to be it.

But is that so bad? The same thing can be said about Newton's first law, which we're quite willing to accept just the way it is. In fact... Newton's first law is just the statement about moving on geodesics applied to flat space - or we could say that the the statement about things moving on geodesics when not subject to external forces is just Newton's first law generalized to curved spacetime.

 

[Markus Hanke]

There's no obvious reason why it has to be that way

Would it make sense to argue that it is due to the principle of least action ? Without that principle, I do not see any mechanism by which free fall world lines would be guaranteed to be spacetime geodesics.

 

[PeterDonis]

I do not see any mechanism by which free fall world lines would be guaranteed to be spacetime geodesics.

There isn't a "mechanism" that does this; it's part of the fundamental rules for how the math of GR is physically interpreted. Free-fall worldlines, which are easily picked out physically by the property that objects following them have zero proper acceleration (which can be measured with an accelerometer) are defined to be geodesics of the spacetime geometry, because that turns out to be the best way to use the math of differential geometry to describe the physics of gravity.

There's no obvious reason why it has to be that way

Not if you're looking for a physical mechanism, no. But that's because the question isn't really about a physical mechanism; it's about how we match up the math of GR with the physics. See above.